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The Regularity of Stochastic Convolution Driven by Tempered Fractional Brownian Motion and Its Application to Mean-field Stochastic Differential Equations
  
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KeyWord:Mean-field stochastic differential equations; Tempered fractional Brownian motion; Caputo fractional derivative; Banach fixed point theorem
Author NameAffiliation
Shang Wu College of Liberal Arts and Science, National University of Defense Technology, Changsha, Hunan 410073, China 
Jianhua Huang College of Liberal Arts and Science, National University of Defense Technology, Changsha, Hunan 410073, China 
Feng Chen School of Science, Changchun University, Changchun, Jilin 130022, China 
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Abstract:
      In this paper, some properties of a stochastic convolution driven by tempered fractional Brownian motion are obtained. Based on this result, we get the existence and uniqueness of stochastic mean-field equation driven by tempered fractional Brownian motion. Furthermore, combining with the Banach fixed point theorem and the properties of Mittag-Leffler functions, we study the existence and uniqueness of mild solution for a kind of time fractional mean-field stochastic differential equation driven by tempered fractional Brownian motion.